where \( I_{(i,j)} \)  is the pixel index and \(\mu _{(i,j)} \)  and \( \sigma _{(i,j)}\)  are the local mean and standard deviation. The NIQE captures the naturalness of a pristine reference image by modelling a generalized gaussian distribution (GGD) [1]}, and models the products of neighbouring pixel coefficients using an Asymmetric GGD (AGGD). The parameters of both the GGD and AGGD are then modelled using a Multivariate Gaussian Model (MVG) distribution [2]}. The quality of the test image is measured in terms of the “distance” of its MVG parameters \(\mu _{t} \)  and \( \sigma _{t}\)  from the pristine MVG parameters obtained. Finally, discriminator gradients computed for both pristine reference and synthesised images are used to compute the distance between the pair.
The expression is given as:
